Recently, along with a current inside a power system becoming complicated, a supply of power of a high reliability and quality has been required and, particularly, there is an increasing need to improve a performance of a frequency measurement apparatus for a power system protection/control apparatus.
The present inventor has already proposed that a response method using a rotation vector on a complex plane is useful in improving a control and protection performance of the power system. This is based on a basic method which represents an alternating voltage as a vector rotating counterclockwise on the complex plane. For example, as described in Patent Document 1 (JP-A-2004-361124), there is a frequency measurement apparatus which is arranged in such a way as to measure a voltage of a power system at a timing of dividing one cycle of a reference wave into equal 4N parts (N is a positive integer), obtain a voltage rotation vector having an apex with the measured voltage as a real part coordinate, and a voltage measured 90 degrees before as an imaginary part coordinate, calculate a chord length of a chord connecting the apex of the voltage rotation vector and an apex of an immediately previous voltage rotation vector, obtain an effective value of voltage from a voltage measured between one timing and an immediately previous cycle of the reference wave, and calculate a frequency of the power system from a phase angle of a voltage rotation vector calculated based on an additional value of the chord length and the effective value of voltage.
FIG. 4, being a diagram of the voltage rotation vector represented on the complex plane, represents a voltage instantaneous value v of the power system as one rotating counterclockwise around an origin 0 on the complex plane. One cycle time of the reference wave is divided into 4N parts (N is an integer), and a time span of one step T is (for example, a 30 electric degree sampling (a sampling of 12 points per cycle) in a 60 Hz system, T=1/60/12=0.00138889 seconds).
A rotation phase angle per step can be calculated as follows.
                              δ          ⁡                      (            t            )                          =                  2          ⁢                                          ⁢                      sin                          -              1                                ⁢                      {                                                            V                  2                                ⁡                                  (                  t                  )                                                            2                ⁢                                  V                  ⁡                                      (                    t                    )                                                                        }                                              (        1        )            
where V(t) is a voltage amplitude, and V2(t) is a chord length facing the rotation phase angle. Supposing that the amplitude and the chord length have been obtained by means of an integration calculation, using one cycle of instantaneous value data, furthermore, a frequency is calculated from a following expression.
                              f          ⁡                      (            t            )                          =                                                            ψ                ⁡                                  (                  t                  )                                                            2                ⁢                π                                      ⁢                          f              0                                =                                                    4                ⁢                                  N                  ·                                      δ                    ⁡                                          (                      t                      )                                                                                                  2                ⁢                π                                      ⁢                          f              0                                                          (        2        )            
where ψ(t) is a rotation phase angle of the voltage rotation vector for one cycle time, and f0 is a reference wave frequency (50 Hz or 60 Hz).
However, as an error occurs in the voltage amplitude and the chord length due to a phase fluctuation such as a voltage fluctuation, it follows that a certain error is also included in a frequency measurement result of Expression (2). As described heretofore, Expression (2) is a so-called static frequency measurement method, and is of high measurement accuracy in a steady state (a sine wave), but the occurrence of the error is inevitable in the event that the phase fluctuation occurs due to the voltage fluctuation or the like. As a method of responding to this, an elimination of an effect of the voltage fluctuation by taking an average value of frequency measurement results for a long time is prevailing at present. For this reason, in this kind of frequency measurement apparatus, a real-time frequency measurement is impossible, affecting a system control/protection apparatus necessary for a high-speed system frequency measurement. It is common knowledge in the industry that a general frequency relay requires a long collation time (for example, a collation time of 90 ms or more in the 60 Hz system).
Patent Document 1: JP-A-2004-361124